Nuclear Magnetic Resonance (NMR) refers to response of nuclear magnetic moments to a combination of static and radio-frequency magnetic fields. These nuclear magnetic moments can interact with externally-applied magnetic fields, producing measurable signals. The hydrogen nucleus has a relatively large magnetic moment and is abundant in both water and hydrocarbon in the pore space of rock. By tuning NMR logging tools to the magnetic resonance frequency of hydrogen, the signal is maximized. NMR signal amplitude is proportional to the number of hydrogen nuclei present and is calibrated to generate signals with amplitude proportional to porosity. The decay of the NMR signal during each measurement cycle is represented by a decay curve M.sub.d (t). This decay curve is related to the underlying distribution of pore sizes. Small pores tend to produce decay at short times, whereas large pores result in decay at long times. Borehole instruments, used in well logging, are capable of measuring the transverse relaxation decay curve. A description of how transverse relaxation is measured and used in the field of oil reservoir identification can be found in U.S. Pat. No. 5,381,092 for "Method and Apparatus for Compressing Data Produced from a Well Tool in a Wellbore Prior to Transmitting the Compressed Data Uphole to a Surface Apparatus" issued to Robert Freedman on Jan. 10, 1995.
NMR, as a well logging technique, does not always yield useful results. Part of the problem with NMR interpretation is a consequence of faulty assumptions, particularly as they apply to carbonate rock. Carbonates are especially troublesome, because their complex microgeometry renders invalid any precise relationship between the T.sub.2 distribution and the pore size distribution. Conventional interpretation of NMR measurements is based on a number of assumptions, to wit:
1. In addition to the bulk relaxation mechanism, magnetization decays because water molecules diffuse to the surface of the grain where they experience an enhanced relaxation rate. This is believed to be a result of their interaction with magnetic fields associated with paramagnetic impurities in the grains.
2. The pore space is divided into separate pores that do not interact with each other. But within each pore, magnetization is assumed to be spatially uniform and to undergo single exponential decay with lifetime T.sub.2. The basis for the latter assumption is that .rho.V.sub.s /D&lt;&lt;1, where D is the diffusion coefficient in the bulk fluid, V.sub.S is the volume-to-surface ratio of the individual pore, and .rho. is the surface relaxivity. The characteristic decay time constant of spin--spin relaxation of any pore is then given as: EQU 1/T.sub.2 =.rho./V.sub.s +1/T.sub.2b
where T.sub.2b is the bulk relaxation time. Note that the above equation establishes a one-to-one relation between the decay rate 1/T.sub.2 for a given pore and the pore size parameter V.sub.s.
3. Based on assumption (2) above, the magnetization decay from the entire rock sample can be represented as the sum of contributions from separate pores. The associated probability volume density function (pvdf) of lifetimes, g(T.sub.2)dT.sub.2 is the fraction of pores whose characteristic T.sub.2 lies between T.sub.2 and T.sub.2 +dT.sub.2, where ##EQU1## The measured NMR signal M.sub.d (t), when normalized to one, can be written as ##EQU2## In practice, the measured signal is inverted to estimate g(T.sub.2). Again, because of assumption 2, g(T.sub.2) is thought to represent the pore size distribution.
The aforementioned (2) and (3) assumptions are flawed in general, and in particular, do not hold for carbonate rocks. The measured decay is not readily translatable to pore Sizes. Inverted T.sub.2 distributions in grain supported carbonates are often unimodal, whereas petrography studies show them to be at least bimodal. Petrographs show that the grains are composed of micrite (microscopic calcite) particles. The pore space between the grains consists of intergranular porosity. The intergranular porosity tends to have pore sizes significantly larger than that of the intragranular porosity. Since these two types of pores of diverse sizes are juxtaposed with a sufficiently large interfacial area between them, the diffusion of magnetic moments between them causes the breakdown of the assumed relationship between the T.sub.2 distribution and the pore size distribution.
In this invention, a new methodology is developed that differs significantly from the conventional approach. The inventive method first considers a model comprising a geometrical arrangement of grains with internal porosity. The NMR relaxation of such a modal is computed by one of several methods discussed hereinafter. The model is reduced to a set of physical parameters which are then adjusted so as to match the relaxation data as well as possible. The result is obtained in terms of these physical parameters, and then integrated with other types of measurements. In the prior art, relaxation data is used directly as the interpretative tool. A T.sub.2 distribution, g(T.sub.2) is estimated from M.sub.d (t) using established signal processing techniques. A pore structure model is then inferred using Assumption 2, above. In this invention, a pore structure model with all of the magnetization relaxation physics included, is used to invert the data. In particular, Assumption 2 is not made; diffusive interaction between pores is allowed and modeled explicitly. Parameters of the model, which represent the pore geometry, are obtained by "best fitting" the model with the data.